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A362194
Number of Grassmannian permutations of size n that avoid a pattern, sigma, where sigma is a pattern of size 7 with exactly one descent.
1
1, 1, 2, 5, 12, 27, 58, 120, 239, 457, 838, 1475, 2498, 4083, 6462, 9934, 14877, 21761, 31162, 43777, 60440, 82139, 110034, 145476, 190027, 245481, 313886, 397567, 499150, 621587, 768182, 942618, 1148985, 1391809, 1676082, 2007293, 2391460, 2835163, 3345578, 3930512
OFFSET
0,3
COMMENTS
A permutation is said to be Grassmannian if it has at most one descent. The definition for sigma is a pattern of size 7 with exactly one descent. For example, sigma can be chosen to be 1247356, 2413567, 3671245, 5712346, etc.
LINKS
Juan B. Gil and Jessica Tomasko, Restricted Grassmannian permutations, ECA 2:4 (2022) Article S4PP6.
FORMULA
a(n) = 1 + Sum_{i=2..6} binomial(n, i).
a(n) = A008859(n) - n.
G.f.: (1-6*x+16*x^2-23*x^3+19*x^4-8*x^5+2*x^6)/(1-x)^7.
E.g.f.: exp(x)*(720 + 360*x^2 + 120*x^3 + 30*x^4 + 6*x^5 + x^6)/720. - Stefano Spezia, Apr 20 2023
PROG
(PARI) a(n) = 1 + sum(i=2, 6, binomial(n, i)) \\ Andrew Howroyd, Apr 20 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jessica A. Tomasko, Apr 20 2023
STATUS
approved